Lasers can be used for cutting an insulation layer of a conductive wire such that a portion of the insulation can be subsequently removed to expose the conductor. Wire is typically wound around a spool and is unwound from the spool as needed. In some instances, the unspooled wire exhibits a “memory” effect, wherein wire curvature is maintained after the wire is unspooled. Such curvature of the wire can make it difficult to center a free end of the wire with respect to cutting laser(s) in a laser wire-processing device. As a result of the wire end being off center relative to the cutting laser(s), the insulation layer may not be cut completely and/or at least a portion of the insulation layer may be cut inadvertently.